paper

No smooth beginning for spacetime

arXiv:1705.00192 · doi:10.1103/PhysRevLett.119.171301

Abstract

We identify a fundamental obstruction to any theory of the beginning of the universe, formulated as a semiclassical path integral. Hartle and Hawking's no boundary proposal and Vilenkin's tunneling proposal are examples of such theories. Each may be formulated as the quantum amplitude for obtaining a final 3-geometry by integrating over 4-geometries. We introduce a new mathematical tool - Picard-Lefschetz theory - for defining the semiclassical path integral for gravity. The Lorentzian path integral for quantum cosmology with a positive cosmological constant is meaningful in this approach, but the Euclidean version is not. Framed in this way, the resulting framework and predictions are unique. Unfortunately, the outcome is that primordial tensor (gravitational wave) fluctuations are unsuppressed. We prove a general theorem to this effect, in a wide class of theories.

arXiv comment2 figures, 1 included in latex file Abstract and introduction rewritten; typos corrected; result extended; responds to arXiv:1705.05340 by Diaz Dorronsoro et al; refers to longer companion paper

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